As a bonus, Sotomayor is even credited with saving baseball. No word yet on her stance on apple pie.

To undo Obama's pick, Republicans will have to uncheck those boxes. It might be possible to argue that Sotomayor either is too liberal or too out of the mainstream, but in making that case, Republicans risk damaging their party's already dismal standing with women and Hispanics. (History check: Last year, Obama won among Hispanics 67 percent to 31 percent.)

Going into this debate, Republicans have been mulling the opportunity and challenges. The math of the Senate makes it likely Obama will get his nominee. As a thoroughly crude political matter, the confirmation seems very secure. Obama already has a nearly filibuster-proof majority with 59 Democrats. It's also unlikely that the two moderate female Republican senators from Maine would vote against Sotomayor. (The two other GOP women might not, either.)

But just because the math points toward confirmation doesn't mean Republicans don't have political opportunities. As Republican Sen. John Cornyn said last week at a breakfast with reporters, his party is traditionally strong on judicial issues. (Of course, he also admitted Republicans are facing extinction.) The nomination offers the opposition a chance to talk about values in a way that reminds conservatives why they like Republicans, and it also allows Republicans a big platform to make the case that the president is on the ideological left. "It's a big television moment," says one senior Senate leadership aide. "It's definitional."

But the nomination and how to respond to it come at a moment when the GOP is having an identity crisis. On the one hand, people like Gen. Colin Powell are arguing that the party should be more inclusive. That means expanding beyond its base in the South and not relying so heavily on its appeal to "Joe the Plumber" types. If Republicans beat up on Sotomayor too much, they might set back this effort.

On the other side of the debate are conservatives like Rush Limbaugh, who will argue the nomination fight provides the perfect opportunity for the party to make proud declarations about what conservatives really believe. That means railing against judges who would legislate from the bench and lambasting the scourge of identity politics, which they see in the Sotomayor pick itself and in her decision in a case involving white firefighters charging the city of New Haven with reverse discrimination.

In early reaction to the pick, Republicans were already targeting what they saw as Sotomayor's judicial activism. "We will thoroughly examine her record to ensure she understands that the role of a jurist in our democracy is to apply the law evenhandedly, despite their own feelings or personal or political preferences," said Senate Minority Leader Mitch McConnell.

The political downside for Obama becomes acute only if Sotomayor is found to be a closet radical in a way that would shock a wide range of people. On the upside, he has answered Latino groups that have been complaining that they are underrepresented in the administration.

Obama knew Sotomayor least well of all the final picks. He met with her last Thursday and was obviously impressed. He made the decision Monday. Describing Obama's process for picking his nominee, senior White House officials refer to his arguments against now-Chief Justice John Roberts. As a senator, Obama said that 95 percent of the issues that come before the court can be decided based on the Constitution and statute. But that remaining 5 percent is disproportionately important, aides say. "The Constitution was written 220 years ago. They had no concept of what we were going to be dealing with," said one aide. "So by definition you have to bring some judgment to it, and his feeling is that judgment should have some view of how real people live."

In announcing the nomination, Obama praised Sotomayor's "practical understanding of how the law works in the everyday lives of the American people" and the "wisdom accumulated from an inspiring life's journey."

Roberts, it turns out, has been a "relentless champion of the overdog," as one senior administration official put it. Sotomayor's presence will not only help stem the court's rightward move (particularly on civil rights cases), but she can also argue for her judicial worldview in public. In addition to "empathy," the much-discussed Obama criterion, that administration official used the term imagination last week in describing what the president was looking for. Obama wanted someone who had the talent to explain the law to the public in plain language.

Obama got a laugh when he said Sotomayor "saved baseball"—she issued the ruling that helped end the strike in 1995—but his underlying point served his message: This is a judge willing to use the law in ways that every American can understand and appreciate.

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